unrealizable

Unrealizable is an adjective describing something that cannot be realized or brought into existence under the given conditions. It is used in everyday language to label plans, goals, or proposals that cannot be achieved in practice because of physical, logical, resource, or policy constraints.

In computing and systems engineering, a specification is unrealizable if no implementation can satisfy it for all allowed inputs or environments. Detecting unrealizability typically involves formal methods such as model checking or synthesis, which attempt to prove the existence of a correct implementation; if none exists, the specification is unrealizable. Addressing unrealizability may involve relaxing requirements, changing assumptions, or decomposing the problem.

In mathematics and graph theory, unrealizable can refer to a sequence that cannot be realized as a graph’s degree sequence. A sequence is graphical if there exists a simple graph with those vertex degrees; criteria such as the Erdős–Gallai theorem or the Havel–Hakimi algorithm decide graphicality. Sequences failing these criteria are unrealizable as degree sequences.

In planning and policy contexts, unrealizable plans may result from overambitious timelines, insufficient resources, or conflicting constraints. Project management often uses feasibility studies to assess realizability and to identify necessary adjustments to goals or constraints.

See also realizability, feasibility, graphical sequence, synthesis, and constraint satisfaction.